Does anyone know who the underbosses were throughout the GF trilogy? I noticed that the FBI had Fredo listed as underboss but I assume they had that wrong.

This topic has come up before with no definitive conclusions. My guess is that Puzo and FFC wanted to stress the familial aspects of the Trilogy, so they dispensed with some of the organizational characteristics usually associated with the Mafia like an underboss. For example, it's unlikely that a Mafia family with as many soldiers as the Corleones would have only two capos most of the time. Fredo's designation by the FBI as an underboss was probably meant to be understood by an audience as a guess by the FBI. But it doesn't make much sense.

I believe it was an authenticity touch on FFC's part:

The chart shown in that scene was an exact replica of the charts shown at the famous Valachi televised hearings in 1962 (see them at the bottom of this url:
http://www.gangrule.com/gallery/maps.html
So was the Senate chamber shown. The FBI had been ignoring the Mafia for decades, so the info in the charts were guesswork on their part. We all know that Fredo really wasn't an underboss. But FFC was trying to show us that the FBI really didn't have a clue as to what was actually happening in the Corleone family.
FFC also had some fun with the chart. If you look it up in Harlan Lebo's "The Godfather Legacy," you'll see some funny names. You'll also see FFC's father in there.

if i was don vito though i would choose sonny or clemenza as my next successor.

is the underboss more powerful than the consligere or no?

An underboss directs street action. He's the operations director in the field. A consigliere gives his advice to the boss. Nevertheless, he can have considerable power and influence depending on how he plays it. I would go with the underboss.

Sonny? No. He ran the family into the ground while Vito was in the hospital. He let his emotions take the best of him.

Sonny didn't run the family into the ground. It's true that by letting his emotions take the best of him he indirectly caused Sollozo's plan to take shape and he eventually cost himself his own life. But if you really anylize the survival of the Corleone family after Vito is shot you realize that Sonny actually did a good job sustaining the family by keeping the other families at bay during the war. As our esteemed friend Turnbull has pointed out, Sonny was a fierce warrior during the war.
He may not have been a good Don overall, but I wouldn't go as far as saying that he ran the Corleone family into the ground.


Don Cardi

so Underboss = Street Boss? (as in the Junior / Tony relationship in Sopranos)

Yes. Junior is still titular head of the Soprano family. But everyone looks to Tony for direction and strategy.

So, is an underboss simply the most influential / powerful caporegime? Or is it an actual appointment?

It's an appointment. In Tony's case, it's by default. Junior is allowed to remain as titular family head in consequence of his attempt to eliminate Tony. That helps to keep some of the heat off Tony.